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Drift-Diffusion Systems: Variational Principles and Fixed Point Maps for
Steady-State Semiconductor Models

#### By: Joseph W. Jerome

The mathematical semiconductor device model, consisting of the potential
equation and the current continuity subsystem for the carriers, is studied
from the standpoint of its decoupling fixed point map and the numerical
approximate fixed point map.
Variational principles will be discussed for this
process and
for discretizations
achieved by use of generalized splines. By the choice of trial space,
these capture the upwinding associated with Scharfetter-Gummel methods.
An approximation calculus
will be introduced in conjunction with the numerical fixed point map.

This paper appeared in:
Computational Electronics (K. Hess, J.P. Leburton and U. Ravaioli, eds.),
Kluwer, 1991, pp. 15--20.

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